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Sunday, April 15, 2007

Leonhard Euler 300

Today is the 300th birthday of Leonhard Euler, the most creative and productive mathematician ever. He grew up in Basel, Switzerland, where he learned the nuts and bolts of the mathematics of his time with the Bernoullis, but left his home town at the age of 20 to never come back, and spent all of his later life in Berlin and Petersburg.

about which whole books have been written. When I was thinking about something a tiny bit original to post about Euler, I thought I might try to trace the origin of this formula in Euler's writings. Mathworld gives as source of the full Euler identity

page 104 of Introductio in Analysin Infinitorum, Vol. 1. Lausanne, 1748. Now, this can be searched for in the Euler Archive, and we find it as entry E101: the Introduction to the Analysis of the Infinite, volume 1, where "Euler lays the foundations of modern mathematical analysis". The original text is available online from gallica.fr, and here is what we read on page 104:

There it is: From this can be seen how imaginary exponential quantities are reduced to sines and cosines of real arguments. It is

I didn't know either until today. You can learn something when writing blog posts ;-)

Though I can't say he is particularly good looking ;-)

He had some kind of infectious desease when he was 31, which caused the loss of his right eye. Later, in 1771, he became even totally blind, and his house in Petersburg burned down. But in spite of all these camalities, he continued working and producing his amazing results.

It seems that he had a quite happy family life. He was married, and the couple had 13 children - five of them survived childhood.

And then all these hundreds of papers he wrote, that's completely crazy...

In the 18th century, European mathematicians Leonhard Euler and Joseph-Louis Lagrange discovered that in this rotating frame there are five gravitational sweet spots, now called Lagrange points. At these equilibrium points, the competing pulls on the third body balance each other, and the body remains motionless.

Euler's Equation unites algebra with analytic geometry. If you do the math you've done the world. Quantum mechanics has no corresponding connection to reality.

Massive resources have been invested to fold gravitation into QFT. Wouldn't it be just like the universe to have success move in the opposite direction... after we get gravitation correct? Organic chemists call this umpolung, and it works.

Arguably the greatest genius to ever live (right there with Newton, Einstein and Gauss)

I think his eulogy sums it up best:

"On the 7th of September 1783, after amusing himself with calculating on a slate the laws of the ascending motion of air balloons, the recent discovery of which was then making a noise all over Europe, he dined with Mr Lexell and his family, talked of Herschel's planet (Uranus), and of the calculations which determine its orbit. A little after, he called his grandchild, and fell a playing with him as he drank tea, when suddenly the pipe, which he held in his hand, dropped from it, and he ceased to calculate and to breathe. The great Euler was no more"